ConverterHub

Arcseconds to Radians Converter

Enter a value in arcseconds to convert it to radians, degrees.

How it is calculated

The angle in arcseconds is multiplied by the exact conversion factor: radians = arcsec × 4.84813681109536×10-6 (that is π ÷ 648,000), and divided by 3600 for degrees: degrees = arcsec ÷ 3600. The radian value is printed in scientific notation with four decimals (for example 4.8481e-6 rad) because arcsecond angles are tiny, and the degree value is rounded to four decimals. Negative angles keep their sign, zero returns zero, and an empty or non-numeric field gives no result.

Worked example

Take an angle of 206265 arcseconds, roughly the size of one radian. Radians: 206265 × 4.84813681×10-6 ≈ 0.99999…, which the tool prints as 1.0000e+0 rad. Degrees: 206265 ÷ 3600 = 57.29583…, shown as 57.2958 °. This agrees with the well-known value of about 57.3 degrees per radian.

Try this example →

Common mistakes

  • Confusing arcseconds with arcminutes. One arcminute is 60 arcseconds, so typing minutes into this field makes the radian result 60 times too small.
  • Misreading scientific notation: 4.8481e-6 means 0.0000048481, not 4.8481.
  • Relying on the degree output for very tiny angles. With four decimals, 0.75 arcsecond shows as 0.0002 °, so the radian figure (3.6361e-6 rad) is the more precise one there.
  • Mixing up arcseconds of angle with seconds of time in right ascension. One second of time equals 15 arcseconds, so the two cannot be swapped.
  • Using the small-angle approximation (angle in radians ≈ sin or tan) for angles that are not small.

About this calculator

An arcsecond is 1/3600 of a degree, the finest unit commonly used to describe tiny angles; converting to the radian — the SI angle unit where a full circle is 2π — gives 1 arcsecond = π/648,000 radians ≈ 4.8481×10⁻⁶ rad.

Astronomers use arcseconds to express stellar parallax, telescope angular resolution, and proper motion (since these angles are naturally tiny), but the underlying physics and optics equations — like the diffraction limit or small-angle approximations — are written in radians, so converting between the two is a routine step in astronomical and optical calculations.

Was this helpful?

You can pick up to 3 reactions.

Comments

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators